A083500 Smallest k such that n*(n+k) + 1 is a cube.

6, 11, 18, 27, 38, 51, 2, 83, 29, 123, 146, 171, 43, 38, 258, 291, 326, 1, 51, 443, 174, 531, 578, 627, 678, 2, 10, 530, 902, 963, 473, 1091, 1158, 1227, 3, 25, 438, 1523, 66, 1683, 1766, 330, 1042, 2027, 46, 2211, 2306, 2403, 70, 2603, 2706, 417, 2918, 73

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003

Keywords

• nonn

Comments

For all n, n*(n+k) + 1 is a square for k = 2.

Differs from A102305 at positions listed by A102306.

Examples

			a(7) = 2 as 7*9 + 1 = 64 = 4^3, though 66 also qualifies but 2<66.
		

Crossrefs

Cf. A083501.

Programs

Mathematica

Do[k = 0; While[i = n(n + k) + 1; !IntegerQ[i^(1/3)], k++ ]; Print[k], {n, 1, 55}]

Extensions

Edited and extended by Robert G. Wilson v, May 11 2003